Abstract

Hybrid dynamical systems are a class of complex systems that involve interacting discrete-event
and continuous-variable dynamics. They are important in applications in embedded systems,
cyber-physical systems, robotics, manufacturing systems, traffic management, bio-molecular networks,
and have recently been at the center of intense research activity in the control theory,
computer-aided verification, and artificial intelligence communities. This paper provides a tutorial
introduction to this multidisciplinary research area. A number of fundamental topics, such as
modeling, abstraction, verification, supervisory control, stability analysis, stabilization, and
optimal control of hybrid systems are introduced and discussed. Additionally, more advanced topics
are briefly discussed at the end of each chapter with references given for further reading.

Hybrid Dynamical Systems

The methods for hybrid systems are distributed across a wide spectrum, ranging from methods known
in the discrete (cyber-)domain at one end, to traditional approaches for the continuous physical
systems at the other. Rooted at opposite ends, both computer scientists and control theorists have
made significant contributions to the field of hybrid systems by extending traditional methods from
the traditional discrete or continuous domain to deal with hybrid systems. However, in general,
there has been little work on integrating methods from these two domains. This is possibly because
the formal methods pursued in computer science traditionally lie in the realm of discrete
mathematics, while control theory approaches lie mainly in the realm of continuous mathematics.

A noticeable trend in the recent hybrid system literature emphasizes the synthesis of hybrid
controllers for continuous or hybrid dynamical systems to satisfy complicated temporal logic
specifications. This is known as symbolic control or hybrid supervisory control, which can be seen
as a crosstalk between these two schools of thoughts.

Hybrid Dynamical Systems balances the emphasis on methods from both computer
science and control theory, and gives the readers a complete picture of the whole field of hybrid
dynamical systems. As well as providing a concise overview for a researcher in the field, the
tutorial style makes it suitable for use in a course and by students.